This study focuses on an analytical investigation of the common characteristics of fatigue models based on a single damage variable. The general single damage variable constitutive equation is used to extract several fundamental properties. It is shown that at constant amplitude loads, damage evolution results are sufficient for predicting fatigue life under any load history. Two-level fatigue envelopes constitute an indirect measure of the damage evolution and form an alternative basis for life prediction. In addition, high-to-low and low-to-high envelopes are anti-symmetrical with respect to each other. A new integral formula for life prediction under random loads is verified with the models of Manson and Hashin, and also developed analytically for other models including Chaboche, resulting in analytical predictions. The Palmgren – Miner rule is found to yield an upper bound for fatigue life predictions under random loads, regardless of the load distribution and the specific single damage variable model.
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